← Linear Algebra

How to solve

u × v = (u₂v₃ − u₃v₂, u₃v₁ − u₁v₃, u₁v₂ − u₂v₁) — the determinant expansion of the symbolic 3×3.

Steps

  1. First component: u₂v₃ − u₃v₂.
  2. Second: u₃v₁ − u₁v₃ (note the order flip).
  3. Third: u₁v₂ − u₂v₁.

Example

(1, 0, 2) × (0, 3, 1)

  1. x: 0·1 − 2·3 = −6.
  2. y: 2·0 − 1·1 = −1.
  3. z: 1·3 − 0·0 = 3.

Answer: (-6, -1, 3)

How to type answers

  • Write vectors like (-6, -1, 3)
Loading drills…